Optical system including multiplexed volume Bragg grating, methods, and applications

Abstract

A method of reversible spatial mode selection and conversion between waveguides and free space is presented using a multiplexed volume Bragg grating (MVBG). The MVBG has an inherent angular selectivity, providing different losses for different transverse modes and converting a higher order mode in waveguide to a single fundamental mode in free space. Using the device in a resonator allows for a pure higher order mode to be guided and amplified in the gain medium, to increase the mode area, to extract accumulated excitation more efficiently, and, therefore, to increase gain of the amplifier. In the same resonator, the device is able to convert the higher order mode to a high brightness Gaussian beam in free space or to a fundamental mode in a waveguide.

We claim: 
     
       1. A method for reversible conversion between fundamental and higher order spatial modes of a propagating optical beam, comprising:
 providing an optical system including:
 a multimode waveguide supporting propagation of a plurality of spatial modes including a fundamental mode and higher-order modes, which said higher-order modes are characterized by two, optical far-field, angularly separated side lobes and by a divergence of each lobe; 
 an imaging system characterized by a magnification coefficient; and 
 a multiplexed volume Bragg grating (MVBG) comprising two (a, b) volume Bragg gratings (VBGs) characterized by an angle, δθ ab , between input Bragg angles of the two VBGs, coincidence of output beams' Bragg angles, and an angular selectivity, δθ a , δθ b , of each VBG; 
 
 propagating a higher order mode beam in the waveguide; 
 imaging an exit facet of the waveguide to the MVBG such that the directions of propagation of converging lobes of the higher order mode coincide with the respective Bragg angles of the VBGs, while the angular divergence of the lobes remains less than the angular selectivity, δθ a , δθ b , of each respective VBG; 
 diffracting the two lobes of the higher-order mode beam in the same direction by the MVBG; and 
 outputting a beam consisting of a fundamental mode. 
 
     
     
       2. The method of  claim 1 , wherein the angular selectivity of the MVBG coincides with or exceeds the divergence of the lobes of the highest order mode imaged to the MVBG. 
     
     
       3. The method of  claim 1 , wherein the waveguide comprises an optical amplifier. 
     
     
       4. The method of  claim 1 , wherein the MVBG is a double transmitting VBG. 
     
     
       5. The method of  claim 1 , wherein the MVBG is a double reflecting VBG. 
     
     
       6. The method of  claim 1 , wherein the step of propagating the higher order mode beam in the waveguide further comprises generating at least some of all of the possible modes in the waveguide each characterized by corresponding two, optical far-field, angularly separated side lobes and by a divergence of each lobe in free space, further comprising:
 imaging the exit facet of the waveguide to the MVBG such that the directions of propagation of converging lobes of one of the propagating higher order modes coincide with the respective Bragg angles of the VBGs, while angular divergence of the lobes remains less than the angular selectivity of each respective VBG; 
 providing a feedback mirror disposed along an optical axis of the output beam; 
 retroreflecting the fundamental mode output beam by the feedback mirror; 
 diffracting the fundamental mode output beam by the MVBG in two directions coinciding with directions of propagation of the side lobes of the previously selected higher order mode in the imaging system; 
 imaging the two side lobes to the front facet of the waveguide; and 
 propagating the only selected higher-order mode in the multimode waveguide. 
 
     
     
       7. The method of  claim 6 , wherein the optical system comprises an optical resonator of a laser. 
     
     
       8. The method of  claim 6 , wherein the MVBG is a double transmitting VBG. 
     
     
       9. The method of  claim 6 , wherein the MVBG is a double reflecting VBG. 
     
     
       10. The method of  claim 6 , wherein the angular selectivity of the MVBG coincides with or exceeds the divergence of the lobes of the highest order mode in the imaging system. 
     
     
       11. A method for reversible conversion between fundamental and several higher order spatial modes of a propagating optical beam, comprising:
 providing an optical system including:
 a multimode waveguide supporting propagation of a plurality of spatial modes including a fundamental mode and higher-order modes, which said higher-order modes are characterized by two, optical far-field, angularly separated side lobes and by a divergence of each lobe; 
 an imaging system characterized by a magnification coefficient; and 
 a MVBG comprising a plurality of pairs (two) of VBGs where each pair is characterized by an angle between input Bragg angles of the two VBGs, an angular selectivity of each VBG, and coincidence of all output beams' Bragg angles; 
 
 propagating a plurality of coherent higher order mode beams in the waveguide; 
 imaging an exit facet of the waveguide to the MVBG such that the directions of propagation of converging lobes of each higher order mode coincide with the respective Bragg angles of the VBGs, while the angular divergence of the lobes remains less than the angular selectivity of each respective VBG; 
 diffracting at least some of the plurality of pairs of the higher-order mode lobes in the same direction by the MVBG; and 
 coherently combining higher order modes to a single outputting a beam consisting of a fundamental mode. 
 
     
     
       12. The method of  claim 11 , wherein the step of propagating the higher order mode beam in the waveguide further comprises generating at least some of all of the possible modes in the waveguide each of which characterized by corresponding two, optical far-field, angularly separated side lobes and by a divergence of each lobe in free space, further comprising:
 imaging the exit facet of the waveguide to the MVBG such that the directions of propagation of converging lobes of at least some of the plurality of the propagating higher order modes coincide with the respective Bragg angles of the pairs of VBGs, while angular divergence of the lobes remains less than the angular selectivity of each respective VBG; 
 providing a feedback mirror disposed along an optical axis of the output beam; 
 retroreflecting the fundamental mode output beam by the feedback mirror; 
 diffracting the fundamental mode output beam by the MVBG in the directions coinciding with directions of propagation of the side lobes of the selected higher order modes in the imaging system; 
 imaging at least some of the plurality of the pairs of side lobes to the front facet of the waveguide; and 
 propagating a selected number of higher-order modes in the multimode waveguide. 
 
     
     
       13. The method of  claim 12 , wherein the optical system comprises an optical resonator of a laser. 
     
     
       14. An optical system, comprising:
 a multimode waveguide having an exit/entrance facet that supports propagation of a plurality of spatial modes including a fundamental mode and higher-order modes, wherein said higher-order modes are characterized by two, optical far-field, angularly separated side lobes and by a divergence of each lobe; 
 an imaging system characterized by a magnification coefficient and disposed so as to image the exit facet of the multimode waveguide; and 
 a multiplexed volume Bragg grating (MVBG) comprising two (a, b) volume Bragg gratings (VBGs) characterized by an angle, δθ ab , between input Bragg angles of the two VBGs, coincidence of output beams' Bragg angles, and an angular selectivity, δθ a , δθ b , of each VBG, disposed in an image plane of the imaging system, 
 
       wherein:
 a) upon (i) propagating a higher order mode beam in the waveguide, (ii) imaging the exit facet of the waveguide to the MVBG such that the directions of propagation of converging lobes of the higher order mode coincide with the respective Bragg angles of the VBGs, while the angular divergence of the lobes remains less than the angular selectivity, δθ a , δθ b , of each respective VBG, and (iii) diffracting the two lobes of the higher-order mode beam in the same direction by the MVBG, a beam consisting of a fundamental mode is output from the system; or 
 b) upon (i) inputting a beam consisting of a fundamental mode to the MVBG, (ii) diffracting the fundamental mode beam by the MVBG in two directions coinciding with directions of propagation of the side lobes of the higher order mode in the imaging system, and (iii) imaging the two side lobes to the entrance facet of the waveguide, a beam comprising at least one higher-order mode characterized by the two imaged side lobes is propagated in the multimode waveguide. 
 
     
     
       15. The optical system of  claim 14 , further comprising a feedback mirror disposed to reflect the output beam consisting of the fundamental mode back through the MVBG. 
     
     
       16. The optical system of  claim 14 , wherein the MVBG is a double transmitting VBG. 
     
     
       17. The optical system of  claim 14 , wherein the MVBG is a double reflecting VBG. 
     
     
       18. The optical system of  claim 14 , comprising an optical resonator of a laser.